The difference of acute angles of a right angled triangle is 72°. Determine these acute angles in circular measure
WBBSE
Class X
Mathematics
Concept of Measurement of Angle
03 Mark
2024
Let the two acute angles of a right-angled triangle be x and y (in degrees).
Since the sum of all angles in a triangle is 180°, and one angle is 90°,
we have
x + y = 90° …(i)
It is given that the difference of the acute angles is 72°,
so,
x – y = 72° …(ii)
Adding (i) and (ii):
2x = 162°
∴ x = 81°
Substitute the value of x in (i):
81° + y = 90°
∴ y = 9°
Now, convert the angles into circular measure (radians):
x = 81° × π \over 180 = 9π \over 20 radians
y = 9° × π \over 180 = π \over 20 radians
Related Questions
More WBBSE Moderate level questions
1/12
Q.
Two unequal arcs of ratio 5 : 2 of a circle subtend angle at the...
A.
Since the angles subtended at the center are proportional to the lengths...
Q.
Express 22°30′ in radians
A.
22°30′ = 22.5° Formula: radians = degrees × 22.5° = 22.5 ×...
Q.
State True or False: The hour hand of a clock rotates through an angle π/3...
A.
True Explanation: Hour hand moves in 12 hours = 360° ⇒ Hour...
Q.
Radius of a circle is 7 cm. Find the angle in radians which is subtended...
A.
Length of arc = 5.5 cm Radius of the circle = 7...
Q.
Write a difference between the geometric angle and trigonometrical angle.
A.
Geometric angle: It is measured in a positive direction from the initial...
Q.
ABCD is a circumscribed quadrilateral of a circle with centre O. Show that AB +...
A.
Given: A quadrilateral ABCD is circumscribed about a circle with centre O....
Q.
If a, b, c are in continued proportion, then prove that, 1/b=1/(b-a) +1/(b-c)
A.
a, b, c are in continued proportion ⇒ b² = ac LHS:...
Q.
If x = √3 + √2 and y = 1/x then find (x + 1/x)²...
A.
x = √3 + √2 ⇒ = = × = = √3...
Q.
If (√a + √b) ∝ (√a-√b) then show that (a + b) ∝ √(ab)
A.
(√a + √b) ∝ (√a-√b) ⇒ (√a + √b) = k (√a-√b)...
Q.
Solve: (2x + 1) + 3/(2x + 1) = 4, (x ≠ −1/2)
A.
Let 2x + 1 = a a + = 4 ⇒ a²...
Q.
Speed of A is 1m/sec more than that of B. A reaches 2 seconds earlier...
A.
Let speed of B = x m/s. Then speed of A =...
Q.
Find the median of the data from the following distribution
A.
Class int Class boundary frequency (f) CF 0 - 9 0 -...